Quantum Structural Theory of Harmony (QSTH M.1A) — Genealogy of Alpha-I-Dim and Equations E1–E10: An Auditable Mathematical Framework

Abstract QSTH M.1A establishes the first auditable mathematical framework of the Quantum Structural Theory of Harmony (QSTH). The publication develops the complete genealogy of Equations E1–E10, beginning with the reference de Sitter realization of Alpha-I-Dim and continuing through a closed sequence of dimensionless structural relations. Throughout the derivation, definitions (DEF), CORE mathematics, CORE-linked physics, and candidate structural interpretations (CAND) are explicitly separated. Rather than proposing a new physical theory, M.1A introduces a reproducible mathematical methodology based on Equation Genealogy, Unit Hygiene, Equation Passports, Quantity Passports, Failure Modes, and Audit I. Every equation is accompanied by an explicit statement of its scope and limitations. Imported quantities such as S_eff and κ(Γ) are intentionally treated as candidate structural objects requiring independent operational definitions in future work. The publication closes the first mathematical skeleton of the QSTH programme (E1–E10) and establishes the methodological foundation for the subsequent volume QSTH M.1B. Description This record contains the Author Edition of QSTH M.1A The publication presents the first coherent mathematical framework within the Quantum Structural Theory of Harmony (QSTH). Its objective is not to introduce a new physical theory, but to establish a disciplined methodology for constructing, auditing and classifying structural mathematical relations. The document introduces: the reference de Sitter realization of Alpha-I-Dim the genealogy of Equations E1–E10 Equation Genealogy Unit Hygiene Equation Passports Quantity Passports Failure Modes Audit I CORE / CORE-linked / CAND separation The mathematical development begins with the dimensionless ratio defining the reference realization of Alpha-I-Dim and derives a consistent sequence of structural identities while maintaining complete dimensional consistency and genealogical traceability. A central methodological principle of M.1A is that mathematical correctness does not by itself imply physical validity. Consequently, every interpretation beyond the explicitly defined CORE layer is identified as CAND and remains subject to future mathematical and empirical justification. The imported quantities S_eff and κ(Γ) are therefore not introduced as established physical observables. They are treated as candidate structural quantities whose operational definitions are intentionally deferred to QSTH M.1B. M.1A concludes with Audit I, documenting the successful closure of the first mathematical skeleton (E1–E10) and preparing the next stage of the mathematical programme. Related Work Note QSTH M.1A begins the mathematical branch of the QSTH publication series. It follows the conceptual foundations established in the earlier QSTH programme while introducing the first fully auditable mathematical framework based on explicit equation genealogy and dimensional discipline. Within the M-Series, M.1A establishes the methodological standards that will remain valid for subsequent publications. The following volume, QSTH M.1B, continues the programme by providing operational definitions for the candidate structural quantities introduced in M.1A, including the configuration space Γ, the effective structural entropy S_eff, and the structural classifier κ(Γ). Plain-language Summary This publication explains how a mathematical framework should be constructed before physical interpretation begins. Rather than asking whether a proposed equation is physically true, M.1A first asks whether it is mathematically traceable, dimensionally consistent, and methodologically auditable. The publication documents the complete derivation of ten structural equations, explains where every definition originates, and clearly separates established mathematics from candidate interpretations. Its principal contribution is therefore a reproducible mathematical methodology, not a claim of empirical confirmation. Final Zenodo Caveat This publication is a mathematical and methodological preprint. It does not claim empirical confirmation of the Quantum Structural Theory of Harmony. It does not introduce new experimentally established laws of physics, nor does it claim that the candidate structural quantities introduced herein possess verified physical meaning. All mathematical derivations are presented within explicitly stated assumptions and are fully auditable through Equation Genealogy, Unit Hygiene and Audit I. Any interpretation beyond the CORE layer remains classified as CAND and requires independent mathematical development and future empirical assessment. Suggested Citation Stepanik, R. (2026). Quantum Structural Theory of Harmony (QSTH M.1A Rev.1) — Genealogy of Alpha-I-Dim and Equations E1–E10: An Auditable Mathematical Framework. Author Edition. Zenodo. Related publications QSTH M.0 QSTH M.1 QSTH M.1B (planned) Landscape of Stable Configurations (planned)